Four-dimensional integrable Hamiltonian systems with simple singular points (topological aspects):
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English Russian |
| Published: |
Providence, R.I.
American Math. Soc.
1998
|
| Series: | Translations of mathematical monographs
176 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus dem Russ. übers. |
| Physical Description: | XII, 177 S. graph. Darst. |
| ISBN: | 0821803751 |
Staff View
MARC
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| 240 | 1 | 0 | |a Četyrechmernye integriruemye Gamil'tonovy sistemy s prostymi osobymi točkami (topologičeskij podchod) |
| 245 | 1 | 0 | |a Four-dimensional integrable Hamiltonian systems with simple singular points (topological aspects) |c L. M. Lerman ; Ya. L. Urmanskiy |
| 264 | 1 | |a Providence, R.I. |b American Math. Soc. |c 1998 | |
| 300 | |a XII, 177 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Translations of mathematical monographs |v 176 | |
| 500 | |a Aus dem Russ. übers. | ||
| 650 | 4 | |a Orbite singulière | |
| 650 | 4 | |a Point singulier | |
| 650 | 7 | |a Systèmes hamiltoniens |2 ram | |
| 650 | 7 | |a Variétés topologiques à 4 dimensions |2 ram | |
| 650 | 4 | |a Four-manifolds (Topology) | |
| 650 | 4 | |a Hamiltonian systems | |
| 700 | 1 | |a Umanskij, Jan L. |e Verfasser |4 aut | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Introduction ix
Chapter 1. General Results of the Theory
of Hamiltonian Systems 1
1.1. Hamiltonian systems on a symplectic manifold 1
1.2. Poisson brackets and first integrals 3
1.3. Integrable systems and Poisson actions 6
1.4. A local structure of the orbit foliation of an action 8
1.5. Formulation of the classification problem for actions and IHVFs 14
Chapter 2. Linear Theory and Classification
of Singular Orbits 17
2.1. Linear Poisson actions 17
2.2. Simple singular points of an action and IHVF (local theory) 26
2.3. One dimensional orbits of the action 28
2.4. Singular trajectories of IHVF 39
Chapter 3. IHVF and Poisson Actions of Morse Type 43
3.1. Limit set of an orbit of the action 43
3.2. Class of Poisson actions and IHVFs of Morse type 45
3.3. General properties of PA of Morse type 46
Chapter 4. Center Center Type Singular Points of PA
and Elliptic Singular Points of IHVF 51
Chapter 5. Saddle Center Type Singular Points 57
5.1. Extended neighborhood of a singular point, and its topology 57
5.2. Isoenergetic equivalence of IHVFs 63
Chapter 6. Saddle Type Singular Points 71
6.1. The degeneracy set 71
6.2. The types of loops and SPTs 73
6.3. Construction of the extended neighborhood 82
6.4. The invariant and formulation of the equivalence theorem 84
6.5. The structure of the auxiliary system and its invariant foliations 86
6.6. The topology of dVe 99
6.7. Proof of the equivalence theorems 107
6.8. The topology of the extended neighborhood V 119
Chapter 7. Saddle Focus Type Singular Points 129
7.1. The structure of a garland and its separatrix set 129
vii
viii CONTENTS
7.2. The structure of the auxiliary gradient system 131
7.3. The construction of the conjugating homeomorphism in U 135
7.4. Proof of the isoenergetic equivalence theorem 137
7.5. The equivalence of actions 145
7.6. The topology of V 145
Chapter 8. Realization 149
8.1. Elliptic points 149
8.2. Singular point of the saddle center type 149
8.3. Singular point of the saddle type 150
8.4. Singular point of the saddle focus type 156
Appendix A. Normal Forms of Quadratic Hamilton Functions and Their
Centralizers in sp(4,R) 163
Appendix B. The Gradient System on M
Compatible with the Hamiltonian 167
Bibliography 175
|
| any_adam_object | 1 |
| author | Lerman, Lev M. Umanskij, Jan L. |
| author_facet | Lerman, Lev M. Umanskij, Jan L. |
| author_role | aut aut |
| author_sort | Lerman, Lev M. |
| author_variant | l m l lm lml j l u jl jlu |
| building | Verbundindex |
| bvnumber | BV013477676 |
| callnumber-first | Q - Science |
| callnumber-label | QA614 |
| callnumber-raw | QA614.83 |
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| callnumber-sort | QA 3614.83 |
| callnumber-subject | QA - Mathematics |
| ctrlnum | (OCoLC)38601786 (DE-599)BVBBV013477676 |
| dewey-full | 514/.74 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514/.74 |
| dewey-search | 514/.74 |
| dewey-sort | 3514 274 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV013477676 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:46:32Z |
| institution | BVB |
| isbn | 0821803751 |
| language | English Russian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009198067 |
| oclc_num | 38601786 |
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| physical | XII, 177 S. graph. Darst. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | American Math. Soc. |
| record_format | marc |
| series | Translations of mathematical monographs |
| series2 | Translations of mathematical monographs |
| spelling | Lerman, Lev M. Verfasser aut Četyrechmernye integriruemye Gamil'tonovy sistemy s prostymi osobymi točkami (topologičeskij podchod) Four-dimensional integrable Hamiltonian systems with simple singular points (topological aspects) L. M. Lerman ; Ya. L. Urmanskiy Providence, R.I. American Math. Soc. 1998 XII, 177 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Translations of mathematical monographs 176 Aus dem Russ. übers. Orbite singulière Point singulier Systèmes hamiltoniens ram Variétés topologiques à 4 dimensions ram Four-manifolds (Topology) Hamiltonian systems Umanskij, Jan L. Verfasser aut Translations of mathematical monographs 176 (DE-604)BV000002394 176 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009198067&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lerman, Lev M. Umanskij, Jan L. Four-dimensional integrable Hamiltonian systems with simple singular points (topological aspects) Translations of mathematical monographs Orbite singulière Point singulier Systèmes hamiltoniens ram Variétés topologiques à 4 dimensions ram Four-manifolds (Topology) Hamiltonian systems |
| title | Four-dimensional integrable Hamiltonian systems with simple singular points (topological aspects) |
| title_alt | Četyrechmernye integriruemye Gamil'tonovy sistemy s prostymi osobymi točkami (topologičeskij podchod) |
| title_auth | Four-dimensional integrable Hamiltonian systems with simple singular points (topological aspects) |
| title_exact_search | Four-dimensional integrable Hamiltonian systems with simple singular points (topological aspects) |
| title_full | Four-dimensional integrable Hamiltonian systems with simple singular points (topological aspects) L. M. Lerman ; Ya. L. Urmanskiy |
| title_fullStr | Four-dimensional integrable Hamiltonian systems with simple singular points (topological aspects) L. M. Lerman ; Ya. L. Urmanskiy |
| title_full_unstemmed | Four-dimensional integrable Hamiltonian systems with simple singular points (topological aspects) L. M. Lerman ; Ya. L. Urmanskiy |
| title_short | Four-dimensional integrable Hamiltonian systems with simple singular points (topological aspects) |
| title_sort | four dimensional integrable hamiltonian systems with simple singular points topological aspects |
| topic | Orbite singulière Point singulier Systèmes hamiltoniens ram Variétés topologiques à 4 dimensions ram Four-manifolds (Topology) Hamiltonian systems |
| topic_facet | Orbite singulière Point singulier Systèmes hamiltoniens Variétés topologiques à 4 dimensions Four-manifolds (Topology) Hamiltonian systems |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009198067&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000002394 |
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